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NDA 1 2024 Maths, question 48

Topic: Trigonometry

Q48

If tan⁡α\tan \alpha and tan⁡β\tan \beta are the roots of the equation x2−6x+8=0x^{2}-6x+8=0, then what is the value of cos⁡(2α+2β)\cos (2\alpha+2\beta) ?

  1. (a) 1375\frac{13}{75}
  2. (b) 1385\frac{13}{85}Correct answer
  3. (c) 1785\frac{17}{85}
  4. (d) 1985\frac{19}{85}

Solution.

Answer: (b) 1385\frac{13}{85}

  1. The sum and product of tan α and tan β are 6 and 8.
  2. Thus tan(α + β) = 6/(1 − 8) = −6/7.
  3. Therefore cos 2(α + β) = (1 − 36/49)/(1 + 36/49) = 13/85.